Question

QUESTION 1 (6 marks) Deposits of $1000 are made into an investment fund at t = 0 and r 1. The fund balance is $1200 just before the deposit at t= 1, and $2200 at 2 (a) [2 marks] Calculate the money-weighted rate of return (MWRR) over the two year period. Express your answer as an effective rate per annum. (b) [2 marks] Calculate the time-weighted rate of return (TWRR) over the two year period. Express your answer as an effective rate per annum. (c) [2 marks] Compare your answers in parts (a) and (b). Is your MWRR greater than, less than, or approximately equal to your TWRR? Provide a written explanation for the relationship between the MWRR and TWRR values you calculated.

Answer 1

1. for MWRR

let MWRR be r

PV of cash inflow = PV of cash outflow

PV of cash inlows is 200/(1+r)^1 + 2200/(1+r)^2

PV of cash outflow is 1000/(1+r)^0 + 1000/(1+r)^1

let (1+r) = x

on equating inflow and outflow we get

200/x + 2200/x^2 = 1000 + 1000/x

on solving for x we get x = 2.75

thus r or MWRR is 2.75-1 = 17.5%

2. TWRR

TWRR = [(1+HPR for period 1) * ( 1+ HPR for period 2)] - 1

where HPR, holding period return is (end value - initial investment + cash flow) / (initial value + cash flow)

HPR1 = (1200 - 1000 + 0) / (1000 + 0) =0.2

HPR 2 = (2200 - 1200 + 1000) / (1200 + 1000) = 0

thus TWRR is [(1 + 0.2) * (1+ 0)] - 1 = 0.2

thus TWRR is 20%

3. TWRR is greater than MWRR as MWRR includes the consideration of periodic cash flows in between the period whereas TWRR excludes that. the reason for the difference is in calculating MWRR there was just 1000 investment amount in first year but 2000 for second year

twrr is the superior measure for calculating public fund managers with no control over the time and size of additional cash flows whereas MWRR is used by private fund managers as they have relative control over the periodic additional cash flows